License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2022.38
URN: urn:nbn:de:0030-drops-158480
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15848/
Go to the corresponding LIPIcs Volume Portal

Jaffke, Lars ; Kwon, O-joung ; Telle, Jan Arne

Classes of Intersection Digraphs with Good Algorithmic Properties

pdf-format:
LIPIcs-STACS-2022-38.pdf (0.9 MB)

Abstract

While intersection graphs play a central role in the algorithmic analysis of hard problems on undirected graphs, the role of intersection digraphs in algorithms is much less understood. We present several contributions towards a better understanding of the algorithmic treatment of intersection digraphs. First, we introduce natural classes of intersection digraphs that generalize several classes studied in the literature. Second, we define the directed locally checkable vertex (DLCV) problems, which capture many well-studied problems on digraphs such as (Independent) Dominating Set, Kernel, and H-Homomorphism. Third, we give a new width measure of digraphs, bi-mim-width, and show that the DLCV problems are polynomial-time solvable when we are provided a decomposition of small bi-mim-width. Fourth, we show that several classes of intersection digraphs have bounded bi-mim-width, implying that we can solve all DLCV problems on these classes in polynomial time given an intersection representation of the input digraph. We identify reflexivity as a useful condition to obtain intersection digraph classes of bounded bi-mim-width, and therefore to obtain positive algorithmic results.

BibTeX - Entry

@InProceedings{jaffke_et_al:LIPIcs.STACS.2022.38,
  author =	{Jaffke, Lars and Kwon, O-joung and Telle, Jan Arne},
  title =	{{Classes of Intersection Digraphs with Good Algorithmic Properties}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{38:1--38:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15848},
  URN =		{urn:nbn:de:0030-drops-158480},
  doi =		{10.4230/LIPIcs.STACS.2022.38},
  annote =	{Keywords: intersection digraphs, H-digraphs, reflexive digraphs, directed domination, directed H-homomorphism}
}

Keywords: intersection digraphs, H-digraphs, reflexive digraphs, directed domination, directed H-homomorphism
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI